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1 Least Squares Equation / Coefficient of Correlation Section 1.3 Prepared by E. Gretchen Gascon

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2 Least Squares Equation / Correlation Coefficient Real data does not very often fall on a straight line when graphed, but we can estimate what the linear equation might be, and then decide how well we did on our estimate. The estimate of the linear equation is called the Least Squares Equation The number that tells us if the estimate is good or not is called the Correlation Coefficient Remember these two terms!

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3 Equation of a line: The standard equation of a line is given by the formula y = m x + b, where (x,y) represents any point on the line. m represents the slope and b the y-value of the y-intercept (0,b) This is called the slope-intercept form of a linear equation.

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4 Equations to use in finding Least Squares Equation Important to have in your notes!

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5 How to find the Least Squares Equation (algebraic method) Start with the ordered pair of data points. Next: find ∑x, ∑y, ∑x², ∑y², ∑xy There are 10 data points, n=10 Substitute into the first equation and solve for m Substitute the expression for b into the second equation Next Slide

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6 How to find the Least Squares Equation (algebraic method) p2 Next: find b. Write the equation of Least Squares using m as the slope, and b as the y-intercept y = x

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7 How to find the Least Squares Equation (Graphing in Excel) How to graph the xy scatter plot, can be seen in the previous presentation “linear equations.” There is also a PDF (Excel graphing) tutorial in the support material. Graphing the ordered pair of point and finding the trend line, yields the same equation.

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8 Formula for Correlation Coefficient Important to have in your notes!

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9 Correlation Coefficient (algebraic method) Substitute the appropriate values into the correlation coefficient equation If r is close to +1 or -1 then the Equation of Least Squares (trend line) is a good fit for the data. If it is close to 0, it is not. The equation found in the previous slide is a good fit.

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10 Correlation Coefficient (Excel method) EITHER: When you graphed the data and created the trend line, check the box Next: Take the square root of r² to find value for r. OR Use the CORREL Excel function

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11 Comments Was there anything about this PowerPoint presentation that you would like explained further? PLEASE CALL Post comments or questions to the Main Forum or your Individual Forum. For more examples be sure to review the Practice Exercises posted in the course materials Forum of our class.

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